Holt Geometry

12-2 Translations12-2 Translations

Holt Geometry

Warm UpWarm UpLesson PresentationLesson PresentationLesson QuizLesson Quiz

Holt Geometry

12-2 TranslationsWarm UpFind the coordinates of the image of ∆ABC with vertices A(3, 4), B(–1, 4), and C(5, –2), after each reflection.

1. across the x-axis

2. across the y-axis

3. across the line y = x

Holt Geometry

12-2 TranslationsWarm UpFind the coordinates of the image of ∆ABC with vertices A(3, 4), B(–1, 4), and C(5, –2), after each reflection.

1. across the x-axisA’(3, –4), B’(–1, –4), C’(5, 2)

2. across the y-axisA’(–3, 4), B’(1, 4), C’(–5, –2)

3. across the line y = xA’(4, 3), B’(4, –1), C’(–2, 5)

Holt Geometry

12-2 Translations

Identify and draw translations.Objective

Holt Geometry

12-2 Translations

A translation is a transformation where all the points of a figure are moved the same distance in the same direction. A translation is an isometry, so the image of a translated figure is congruent to the preimage.

Holt Geometry

12-2 TranslationsExample 1: Identifying Translations

Tell whether each transformation appears to be a translation. Explain.

No; the figure appears to be flipped.

Yes; the figure appears to slide.

A. B.

Holt Geometry

12-2 TranslationsCheck It Out! Example 1

Tell whether each transformation appears to be a translation.a. b.

No; not all of the points have moved the same distance.

Yes; all of the points have moved the same distance in the samedirection.

Holt Geometry

12-2 TranslationsDefinition of a Vector

Holt Geometry

12-2 Translations

Holt Geometry

12-2 TranslationsExample 2: Drawing Translations

Copy the quadrilateral and the translation vector. Draw the translation along

Step 1 Draw a line parallel to the vector through each vertex of the triangle.

Holt Geometry

12-2 TranslationsExample 2 Continued

Step 2 Measure the length of the vector. Then, from each vertex mark off the distance in the same direction as the vector, on each of the parallel lines.

Step 3 Connect the images ofthe vertices.

Holt Geometry

12-2 TranslationsCheck It Out! Example 2

Copy the quadrilateral and the translation vector. Draw the translation of the quadrilateral along

Step 1 Draw a line parallel to the vector through each vertex of the quadrangle.

Holt Geometry

12-2 TranslationsCheck It Out! Example 2 Continued

Step 2 Measure the length of the vector. Then, from each vertex mark off this distance in the same direction as the vector, on each of the parallel lines.

Step 3 Connect the imagesof the vertices.

Holt Geometry

12-2 Translations

Recall that a vector in the coordinate plane can be written as <a, b>, where a is the horizontal change and b is the vertical change from the initial point to the terminal point.

Holt Geometry

12-2 Translations

Holt Geometry

12-2 TranslationsDraw the image of triangle ABC, A(2,3), B(-1,4) , and C(-2,-4) translated 3 unit right or

vector <3,0>.

Holt Geometry

12-2 TranslationsDraw the image of triangle ABC, A(2,3), B(-1,4) , and C(-2,-4) translated 3 down or with

vector <0,-3>.

Holt Geometry

12-2 TranslationsDraw the image of triangle ABC, A(2,3), B(-1,4) , and C(-2,-4) translated 2 unit right and 1

unit down .

Holt Geometry

12-2 TranslationsExample 3: Drawing Translations in the Coordinate Plane

Translate the triangle with vertices D(–3, –1), E(5, –3), and F(–2, –2) along the vector <3, –1>.

The image of (x, y) is (x + 3, y – 1).D(–3, –1) D’(–3 + 3, –1 – 1)

= D’(0, –2)E(5, –3) E’(5 + 3, –3 – 1)

= E’(8, –4)F(–2, –2) F’(–2 + 3, –2 – 1)

= F’(1, –3)Graph the preimage and the image.

Holt Geometry

12-2 TranslationsCheck It Out! Example 3

Translate the quadrilateral with vertices R(2, 5), S(0, 2), T(1,–1), and U(3, 1) along the vector <–3, –3>. The image of (x, y) is (x – 3, y – 3).R(2, 5) R’(2 – 3, 5 – 3)

= R’(–1, 2)S(0, 2) S’(0 – 3, 2 – 3)

= S’(–3, –1)T(1, –1) T’(1 – 3, –1 – 3)

= T’(–2, –4)U(3, 1) U’(3 – 3, 1 – 3)

= U’(0, –2)Graph the preimage and the image.

R

S

T

UR’

S’

T’

U’

Holt Geometry

12-2 TranslationsLesson Quiz: Part I

1. Tell whether the transformation appears to be a translation.

yes

2. Copy the triangle and the translation vector. Draw the translation of the triangle along

Holt Geometry

12-2 TranslationsHomework

Translate the figure with the given vertices along the given vector. Use the graph paper to graph.

2. G(8, 2), H(–4, 5), I(3,–1); <–2,0>

3. S(0, –7), T(–4, 4), U(–5, 2), V(8, 1); <–4, 5>

1. Translate the triangle ABC A(-1,3), B(3,0), and C(2,4) 3 units left and 2 units down.

Holt Geometry

12-2 TranslationsLesson Quiz: Part III

5. A rook on a chessboard has coordinates (3, 4). The rook is moved up two spaces. Then it is moved three spaces to the left. What is the rook’s final position? What single vector moves the rook from its starting position to its final position?